Double copy in AdS3 from minitwistor space

Abstract

The double copy relates gravitational theories to the square of gauge theories. While it is well understood in flat backgrounds, its precise realisation around curved spacetimes remains an open question. In this paper, we construct a classical double copy for cohomology class representatives in the minitwistor space of hyperbolic spacetimes. We find that the realisation of a physical double copy requires that the masses of the different spinning fields are not equal, contrary to the flat space prescription. This leads to a position-space double copy for bulk-to-boundary propagators. We also show that in coordinate space, this implies the Cotton double copy for waves and warped black holes of Topologically Massive Gravity. We show that these are exact double copy relations by constructing their Kerr-Schild metrics and also analysing the Kerr-Schild double copy. Furthermore, we find that near the boundary the double copy relates the dual CFT currents.